In this work, we design explicit, finite-dimensional boundary feedback laws for stabilisation to trajectories for parabolic-type equations. The simple form of the feedback allows to write the solution of the corresponding closed-loop equation in a mild formulation via a kernel; then, taking advantage of this, the stability is shown. As an application, null stabilisation for stochastic parabolic-type equations is deduced as well. As far as we know, the present work is the first result on boundary feedback stabilisation to trajectories and for stochastic parabolic-type equations, with stability guaranteed independent of how large the level of the noise is.